Lightroom and other CC apps displaying incorrect cloud storage space remaining

It depends on what you are wanting to achieve. If you just want viewing and light-editing access to your images when mobile, then many Classic-based users are simply syncing smart previews to the cloud: initial upload is much quicker, they are less demanding in terms of space taken on the mobile device, and of course they are stored in the cloud for free. The main thing that you cannot do with this method is export full resolution files when mobile.

If, OTOH, you specifically do want your originals in the cloud, there are only two ways to achieve that....one is by catalog migration, the other is by direct import into one of the cloudy apps. I understand the point about existing collections, but avoidance of recreating those in Lightroom after the originals have been uploaded is still possible using either method.

Catalog migration is the more straightforward method, but there is one potential issue if you intend to continue to sync the Classic catalog after migration.....that scenario is not encouraged by Adobe, one of the reasons being that there might be some oddities (in Classic) after you renable sync in Classic. In theory, when that sync is re-enabled Classic should check with the cloud and realise all the Classic assets are already in the cloud and thus add them all to All Synced Photographs, i.e. all images in Classic will be synced. In practice, however, it's possible that if some of the originals weren't initally synced before migration then Classic will leave those originals unsynced, and instead create virtual copies of them. The result is some originals are not synced, yet have virtual copies which are synced. That can get very confusing. My advice to you is that if you decide to do the catalog migration, you might want to consider syncing all the Classic images as smart previews first.

The other method uses an undocumented "feature". If Classic images have been synced as smart previews, subsequently importing those same images directly into Lightroom should result in those originals being uploaded to the cloud and replacing the existing smart previews. In Lightroom the sync status icon will change to reflect that swap, but there's no impact in Classic other than it now knows that the original is in the cloud, rather than the smart preview. One consequence of that is that if in Classic you subsequently save metadata to any of your images, all non-proprietary raw files are physically updated and that will trigger a resync of that original. That in turn will cause a syncing problem if any of those image files exceed 200MB (e.g. pano DNGs, layered Tiffs), as Classic cannot sync files larger than that 200MB limit.

Whichever method you use, going forward you'd probably be wanting to import new originals directly into Lightroom, and allowing them to sync down as originals into Classic. That means that Classic would store those images in a date-based folder structure, which may or may not be an issue.

Just think carefully about this. The smart previews-only method is far simpler to manage, as well as being cheaper, the hybrid method (using Classic and the Cloud to manage synced originals) gets the originals into the cloud but is more difficult to manage.....understanding the whole syncing process, and its foibles, would be key.